A theoretical basis for cell death

Understanding deaths and life-death boundaries of cells is a fundamental challenge in biological sciences. In this study, we present a theoretical framework for investigating cell death. We conceptualize cell death as a controllability problem within dynamical systems, and compute the life-death boundary through the development of "stoichiometric rays". This method utilizes enzyme activity as control parameters, exploiting the inherent property of enzymes to enhance reaction rates without affecting thermodynamic potentials. This approach facilitates the efficient evaluation of the global controllability of models. We demonstrate the utility of our framework using its application to a toy metabolic model, where we delineate the life-death boundary. The formulation of cell death through mathematical principles provides a foundation for the theoretical study of cellular mortality. SIGNIFICANCE STATEMENTWhat is death? This fundamental question in biology lacks a clear theoretical framework despite numerous experimental studies. In this study, we present a new way to understand cell death by looking at how cells can or cannot control their states. We define a "dead state" as a state from which a cell cannot return to being alive. Our method, called "Stoichiometric Rays", helps determine if a cells state is dead based on enzymatic reactions. By using this method, we can quantify the life-death boundary in metabolic models. The present framework provides a theoretical basis and a tool for understanding cell death.